Preheat your oven to 350°F (180°C). Prepare a 9x13 inch cake pan by greasing it with non-stick baking spray and lining it with parchment paper that extends over the edges for easy removal later.

In a medium bowl, combine the flour, baking powder, and salt, whisking them together. Set this mixture aside.

In a large mixing bowl, blend the melted butter and sugar until they are well mixed. Then, add the eggs and vanilla extract, continuing to mix until everything is combined.

Incorporate the dry ingredients into the wet mixture, stirring until just combined. Be careful not to overmix; the batter will be thick.

Spread the batter evenly in the bottom of the prepared cake pan and set it aside.

For the topping, beat the cream cheese with half of the powdered sugar until smooth and well combined. Gradually add the remaining powdered sugar and mix until fully incorporated.

Add the eggs one at a time, mixing well and scraping down the sides of the bowl after each addition. Then, mix in the vanilla extract and melted butter until everything is well combined.

Pour the cream cheese mixture over the cake batter in the pan, spreading it into an even layer.

Bake in the preheated oven for 30-40 minutes, or until the top is lightly golden and has formed a light crust.

Once baked, remove the cake from the oven and let it cool at room temperature. You can serve it warm or refrigerate it until firm for easier slicing. Store any leftovers in the fridge for up to 4-5 days, and enjoy it either chilled or at room temperature.